The largest 3-digit number has a 9-digit cube and a 9-digit number can have a sod of at most 9*6=54, which has only two digits; other cubes of 3-digit numbers are even smaller. The largest 4-digit number has 12 digits and their largest sod, even in theory, can only be 9*12=108, a 3-digit number. This continues, so that n can have no more than two digits and the above program tests all 2-digit numbers, so that the list is complete.